Question

suppose that $2000 is loaned at a rate of 13.5%, compounded annually. assuming that no payments are made, find the amount owed after 8 years. do not round any intermediate computations, and round your answer to the nearest cent.

Explanation:

Step1: Identify compound interest formula

The formula for compound amount is $A = P(1 + r)^t$, where:

• $P$ = principal amount, $r$ = annual interest rate (decimal), $t$ = time in years

Step2: Convert rate to decimal

$r = \frac{13.5}{100} = 0.135$

Step3: Plug values into formula

$A = 2000(1 + 0.135)^8$

Step4: Calculate the growth factor

$1 + 0.135 = 1.135$; $1.135^8 \approx 2.8179$

Step5: Compute final amount

$A = 2000 \times 2.8179 = 5635.80$

Answer:

$\$5635.80$